Numerical Method of Hybrid Stochastic Functional Differential Equations with the Local Lipschitz Coefficients

Hua Yang; Feng Jiang; Jun Hao Hu

doi:10.4028/www.scientific.net/AMR.267.422

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HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 267Numerical Method of Hybrid Stochastic Functional...

Numerical Method of Hybrid Stochastic Functional Differential Equations with the Local Lipschitz Coefficients

Abstract:

Recently, hybrid stochastic differential equations have received a great deal of attention. It is surprising that there are not any numerical schemes established for the hybrid stochastic functional differential equations. In this paper, the Euler—Maruyama method is developed, and the main aim is to show that the numerical solutions will converge to the true solutions under the local Lipschitz condition. The result obtained generalizes the earlier results.